Question

How do you normalize `(5i- 3j + 12k)`?

Answer 1

Normalizing a vector creates a 'unit vector' 1 unit in length in the same direction as the original vector. In this case the normalized vector is `(5/sqrt178i-3/sqrt178j+12/sqrt178k)` or `(5/13.3i-3/13.3j+12/13.3k)`

Explanation:

Normalizing a vector means dividing each of the elements by the length of the vector.

The length of this vector is `l=sqrt(5^2+(-3)^2+12^2)=sqrt178~~13.3`.

The normalized vector can be represented as `(5/sqrt178i-3/sqrt178j+12/sqrt178k)` or `(5/13.3i-3/13.3j+12/13.3k)`.